Search results for: polynomial basis

Authors: Kushakov Kholmurodjon, Muhammadjonov Akbarshox

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This present paper is devoted to a system of second-order nonlinear differential equations with a special right-hand side, exactly, the linear part and a third-order polynomial of a special form. It is shown that for some relations between the parameters, there is a second-order curve in which trajectories leaving the points of this curve remain in the same place. Thus, the curve is invariant with respect to the given system. Moreover, this system is invariant under a non-degenerate linear transformation of variables. The form of this curve, depending on the relations between the parameters and the eigenvalues of the matrix, is proved. All solutions of this system of differential equations are shown analytically.

Keywords: dynamic system, ellipse, hyperbola, Hess system, polar coordinate system

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Authors: S. Ghammamy, M. Mirzaabdollahiha

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Quantum mechanical calculations of energies, geometries, and vibrational wavenumbers of fluorous 1,3-dion compounds are carried out using density functional theory (DFT/B3LYP) method with LANL2DZ basis sets. The calculated HOMO and LUMO energies show that charge transfer occurs in the molecules. The thermodynamic functions of fluorous 1,3-dion compounds have been performed at B3LYP/LANL2DZ basis sets. The theoretical spectrograms for F NMR spectra of fluorous 1,3-dion compounds have also been constructed. The F NMR nuclear shieldings of fluoride ligands in fluorous 1,3-dion compounds have been studied quantum chemical.

Keywords: density function theory, natural bond orbital, HOMO, LOMO, fluorous

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Authors: Eze R. Onukwugha

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The presence of cyanide in wastewater is known to inhibit the normal functioning of bio-reactors since it has the tendency to poison reactor micro-organisms. Bench scale models of activated sludge reactors with varying aspect ratios were operated for the treatment of cassava wastewater at several values of hydraulic retention time (HRT). The different values of HRT were achieved by the use of a peristaltic pump to vary the rate of introduction of the wastewater into the reactor. The main parameters monitored are the cyanide concentration and respective COD values of the influent and effluent. These observed values were then transformed into a mathematical model for the prediction of treatment efficiency.

Keywords: wastewater, aspect ratio, cyanide-inhibited wastewater, modeling

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Authors: Kirill Trapezon, Alexandr Trapezon

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A problem is formulated for the natural oscillations of a circular plate of linearly variable thickness on the basis of the symmetry method. The equations of natural frequencies and forms for a plate are obtained, providing that it is rigidly fixed along the inner contour. The first three eigenfrequencies are calculated, and the eigenmodes of the oscillations of the acoustic element are constructed. An algorithm for applying the symmetry method and the factorization method for solving problems in the theory of oscillations for plates of variable thickness is shown. The effectiveness of the approach is demonstrated on the basis of comparison of known results and those obtained in the article. It is shown that the results are more accurate and reliable.

Keywords: vibrations, plate, method of symmetries, differential equation, factorization, approximation

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Authors: S. B. Provost, Hossein Zareamoghaddam

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A univariate density approximation technique whereby the derivative of the logarithm of a density function is assumed to be expressible as a rational function is introduced. This approach which extends Pearson’s curve system is solely based on the moments of a distribution up to a determinable order. Upon solving a system of linear equations, the coefficients of the polynomial ratio can readily be identified. An explicit solution to the integral representation of the resulting density approximant is then obtained. It will be explained that when utilised in conjunction with sample moments, this methodology lends itself to the modelling of ‘big data’. Applications to sets of univariate and bivariate observations will be presented.

Keywords: density estimation, log-density, moments, Pearson's curve system

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Authors: Liu Haitao, Wang Hengyong

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This paper attempts to kayak, Zhaoqing City, the annual training program for young men, the deconstruction and analysis, describe the characteristics of their training load, Young people to extract the key issues for training kayak, kayak training young people to clarify in Zhaoqing City, and the cause of the bottlenecks. On one hand, scientifically arranging for the coaches to adjust training load and provide the basis for periodic structure, for young people to provide practical reference kayak athletes. On the other hand, through their training load research, enrich the theoretical system kayak training project for junior kayak athletes to provide a theoretical basis.

Keywords: juniors, kayak, training programs, full year

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Authors: Sheila S. Silang

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This research seeks to make an impact analysis on multiple intelligence as the basis for differentiated classroom instruction in TLE. It will also address the felt need of how TLE subject could be taught effectively exhausting all the possible means.This study seek the effect of giving different instruction according to the ability of the students in the following objectives: 1. student’s technological skills enhancement, 2. learning potential improvements 3. having better linkage between school and community in a need for soliciting different learning devices and materials for the learner’s academic progress. General Luna, Quezon is composed of twenty seven barangays. There are only two public high schools. We are aware that K-12 curriculum is focused on providing sufficient time for mastery of concepts and skills, develop lifelong learners, and prepare graduates for tertiary education, middle-level skills development, employment, and entrepreneurship. The challenge is with TLE offerring a vast area of specializations, how would Multiple Intelligence play its vital role as basis in classroom instruction in acquiring the requirement of the said curriculum? 1.To what extent do the respondent students manifest the following types of intelligences: Visual-Spatial, Body-Kinesthetic, Musical, Interpersonal, Intrapersonal, Verbal-Linguistic, Logical-Mathematical and Naturalistic. What media should be used appropriate to the student’s learning style? Visual, Printed Words, Sound, Motion, Color or Realia 3. What is the impact of multiple intelligence as basis for differentiated instruction in T.L.E. based on the following student’s ability? Learning Characteristic and Reading Ability and Performance 3. To what extent do the intelligences of the student relate with their academic performance? The following were the findings derived from the study: In consideration of the vast areas of study of TLE, and the importance it plays in the school curriculum coinciding with the expectation of turning students to technologically competent contributing members of the society, either in the field of Technical/Vocational Expertise or Entrepreneurial based competencies, as well as the government’s concern for it, we visualize TLE classroom teachers making use of multiple intelligence as basis for differentiated classroom instruction in teaching the subject .Somehow, multiple intelligence sample such as Linguistic, Logical-Mathematical, Bodily-Kinesthetic, Interpersonal, Intrapersonal, and Spatial abilities that an individual student may have or may not have, can be a basis for a TLE teacher’s instructional method or design.

Keywords: education, multiple, differentiated classroom instruction, impact analysis

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Authors: A. Belmeguenai, K. Mansouri, R. Djemili

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This work present a new algorithm based on the nonlinear filter generator for speech encryption and decryption. The proposed algorithm consists on the use a linear feedback shift register (LFSR) whose polynomial is primitive and nonlinear Boolean function. The purpose of this system is to construct Keystream with good statistical properties, but also easily computable on a machine with limited capacity calculated. This proposed speech encryption scheme is very simple, highly efficient, and fast to implement the speech encryption and decryption. We conclude the paper by showing that this system can resist certain known attacks.

Keywords: nonlinear filter generator, stream ciphers, speech encryption, security analysis

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Authors: Sammani Danwawu Abdullahi

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Vertex Enumeration Algorithms explore the methods and procedures of generating the vertices of general polyhedra formed by system of equations or inequalities. These problems of enumerating the extreme points (vertices) of general polyhedra are shown to be NP-Hard. This lead to exploring how to count the vertices of general polyhedra without listing them. This is also shown to be #P-Complete. Some fully polynomial randomized approximation schemes (fpras) of counting the vertices of some special classes of polyhedra associated with Down-Sets, Independent Sets, 2-Knapsack problems and 2 x n transportation problems are presented together with some discovered open problems.

Keywords: counting with uncertainties, mathematical programming, optimization, vertex enumeration

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Authors: Eyad Almaita

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In this paper, a novel adaptive Radial Basis Function Neural Networks (RBFNN) algorithm is used to forecast the hour by hour electrical load demand in Jordan. A small and effective RBFNN model is used to forecast the hourly total load demand based on a small number of features. These features are; the load in the previous day, the load in the same day in the previous week, the temperature in the same hour, the hour number, the day number, and the day type. The proposed adaptive RBFNN model can enhance the reliability of the conventional RBFNN after embedding the network in the system. This is achieved by introducing an adaptive algorithm that allows the change of the weights of the RBFNN after the training process is completed, which will eliminates the need to retrain the RBFNN model again. The data used in this paper is real data measured by National Electrical Power co. (Jordan). The data for the period Jan./2012-April/2013 is used train the RBFNN models and the data for the period May/2013- Sep. /2013 is used to validate the models effectiveness.

Keywords: load forecasting, adaptive neural network, radial basis function, short-term, electricity consumption

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Authors: Ceren Kaya, Okan Erkaymaz, Orhan Ayar, Mahmut Özer

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Diabetes Mellitus (Diabetes) is a disease based on insulin hormone disorders and causes high blood glucose. Clinical findings determine that diabetes can be diagnosed by electrophysiological signals obtained from the vital organs. 'Diabetic Retinopathy' is one of the most common eye diseases resulting on diabetes and it is the leading cause of vision loss due to structural alteration of the retinal layer vessels. In this study, features of horizontal and vertical Video-Oculography (VOG) signals have been used to classify non-proliferative and proliferative diabetic retinopathy disease. Twenty-five features are acquired by using discrete wavelet transform with VOG signals which are taken from 21 subjects. Two models, based on multi-layer perceptron and radial basis function, are recommended in the diagnosis of Diabetic Retinopathy. The proposed models also can detect level of the disease. We show comparative classification performance of the proposed models. Our results show that proposed the RBF model (100%) results in better classification performance than the MLP model (94%).

Keywords: diabetic retinopathy, discrete wavelet transform, multi-layer perceptron, radial basis function, video-oculography (VOG)

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Authors: Mahdi Ebrahimi

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One of the most effective factors that can empower and modernize the Islamic government according to the needs of society is the institution of expediency in Islamic governance. At the same time, not paying attention to the foundations and principles of Islamic governance may cause this factor to create the basis for corruption and totalitarianism of the rulers, which ultimately causes a gap between the people and the rulers and the emergence of whole government corruption and dictatorship. Meanwhile, there are specific principles in the doctrine of Islamic Governance that can prevent such an event from happening. Principles such as: remaining popular and pious by the Ulama, Amr Bil-Maroof Va Nahy An Al-Munkar (commanding the good and preventing the bad) by the individuals, the rule of frank criticism with loud voices and clarification and accountability in the fields that cause the corruption of those in charge. In this research, these principles are presented along with their Islamic basis. It is also stated what effect each of these cases will have on preserving Islam in the ruling system.

Keywords: expediency, Islamic ruling, Islamic principles, Islam

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Authors: Choukri Lekbir, Mira Mokhtari

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Hydrogen-Materials interaction and mechanisms can be modeled at nano scale by quantum methods. In this work, the effect of hydrogen on the electronic properties of a cluster material model «nickel» has been studied by using of density functional theoretical (DFT) method. Two types of clusters are optimized: Nickel and hydrogen-nickel system. In the case of nickel clusters (n = 1-6) without presence of hydrogen, three types of electronic structures (neutral, cationic and anionic), have been optimized according to three basis sets calculations (B3LYP/LANL2DZ, PW91PW91/DGDZVP2, PBE/DGDZVP2). The comparison of binding energies and bond lengths of the three structures of nickel clusters (neutral, cationic and anionic) obtained by those basis sets, shows that the results of neutral and anionic nickel clusters are in good agreement with the experimental results. In the case of neutral and anionic nickel clusters, comparing energies and bond lengths obtained by the three bases, shows that the basis set PBE/DGDZVP2 is most suitable to experimental results. In the case of anionic nickel clusters (n = 1-6) with presence of hydrogen, the optimization of the hydrogen-nickel (anionic) structures by using of the basis set PBE/DGDZVP2, shows that the binding energies and bond lengths increase compared to those obtained in the case of anionic nickel clusters without the presence of hydrogen, that reveals the armor effect exerted by hydrogen on the electronic structure of nickel, which due to the storing of hydrogen energy within nickel clusters structures. The comparison between the bond lengths for both clusters shows the expansion effect of clusters geometry which due to hydrogen presence.

Keywords: binding energies, bond lengths, density functional theoretical, geometry optimization, hydrogen energy, nickel cluster

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Authors: Leizhang Wang, Baocang Wang

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General Sieve Kernel (G6K) is considered as currently the fastest algorithm for the shortest vector problem (SVP) and record holder of open SVP challenge. We study the lattice basis quality improvement effects of the Workout proposed in G6K, which is composed of a series of pumps to solve SVP. Firstly, we use a low-dimensional pump output basis to propose a predictor to predict the quality of high-dimensional Pumps output basis. Both theoretical analysis and experimental tests are performed to illustrate that it is more computationally expensive to solve the LWE problems by using a G6K default SVP solving strategy (Workout) than these lattice reduction algorithms (e.g. BKZ 2.0, Progressive BKZ, Pump, and Jump BKZ) with sieving as their SVP oracle. Secondly, the default Workout in G6K is optimized to achieve a stronger reduction and lower computational cost. Thirdly, we combine the optimized Workout and the Pump output basis quality predictor to further reduce the computational cost by optimizing LWE instances selection strategy. In fact, we can solve the TU LWE challenge (n = 65, q = 4225, = 0:005) 13.6 times faster than the G6K default Workout. Fourthly, we consider a combined two-stage (Preprocessing by BKZ- and a big Pump) LWE solving strategy. Both stages use dimension for free technology to give new theoretical security estimations of several LWE-based cryptographic schemes. The security estimations show that the securities of these schemes with the conservative Newhope’s core-SVP model are somewhat overestimated. In addition, in the case of LAC scheme, LWE instances selection strategy can be optimized to further improve the LWE-solving efficiency even by 15% and 57%. Finally, some experiments are implemented to examine the effects of our strategies on the Normal Form LWE problems, and the results demonstrate that the combined strategy is four times faster than that of Newhope.

Keywords: LWE, G6K, pump estimator, LWE instances selection strategy, dimension for free

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Authors: Likewin Thomas, M. V. Manoj Kumar, B. Annappa

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The aim of this study was to develop an Artificial Neural Network0 s recommendation model for an online process using the complexity of load, performance, and average servicing time of the resources. Here, the proposed model investigates the resource performance using stochastic gradient decent method for learning ranking function. A probabilistic cost function is implemented to identify the optimal θ values (load) on each resource. Based on this result the recommendation of resource suitable for performing the currently executing task is made. The test result of CoSeLoG project is presented with an accuracy of 72.856%.

Keywords: ADALINE, neural network, gradient decent, process mining, resource behaviour, polynomial regression model

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Authors: Dariusz Jacek Jakóbczak

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Mathematics and computer science are interested in methods of 2D curve interpolation and extrapolation using the set of key points (knots). A proposed method of Hurwitz- Radon Matrices (MHR) is such a method. This novel method is based on the family of Hurwitz-Radon (HR) matrices which possess columns composed of orthogonal vectors. Two-dimensional curve is interpolated via different functions as probability distribution functions: polynomial, sinus, cosine, tangent, cotangent, logarithm, exponent, arcsin, arccos, arctan, arcctg or power function, also inverse functions. It is shown how to build the orthogonal matrix operator and how to use it in a process of curve reconstruction.

Keywords: 2D data interpolation, hurwitz-radon matrices, MHR method, probabilistic modeling, curve extrapolation

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Authors: Mohammad Heidari

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In this paper a method for high strength steel is proposed of residual stresses in autofrettaged tubes by combination of artificial neural networks is presented. Many different thick walled cylinders that were subjected to different conditions were studied. At first, the residual stress is calculated by analytical solution. Then by changing of the parameters that influenced in residual stresses such as percentage of autofrettage, internal pressure, wall ratio of cylinder, material property of cylinder, bauschinger and hardening effect factor, a neural network is created. These parameters are the input of network. The output of network is residual stress. Numerical data, employed for training the network and capabilities of the model in predicting the residual stress has been verified. The output obtained from neural network model is compared with numerical results, and the amount of relative error has been calculated. Based on this verification error, it is shown that the radial basis function of neural network has the average error of 2.75% in predicting residual stress of thick wall cylinder. Further analysis of residual stress of thick wall cylinder under different input conditions has been investigated and comparison results of modeling with numerical considerations shows a good agreement, which also proves the feasibility and effectiveness of the adopted approach.

Keywords: thick walled cylinder, residual stress, radial basis, artificial neural network

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Authors: Aman Ullah Khan, Muhammad Younus, Aqil Ijaz, Muti-Ur-Rehman Khan, Sayyed Aun Muhammad, Asif Idrees, Sanan Raza, Amar Nasir

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Dengue fever and malaria are important vector-borne diseases of public health significance affecting millions of people around the globe. Dengue fever is caused by Dengue virus while malaria is caused by plasmodium protozoan. Generally, the consequences of Malaria are less severe compared to dengue fever. This study was designed to differentiate dengue fever and malaria on the basis of clinical and laboratory findings and to compare the changes in both diseases having different causative agents transmitted by the common vector. A total of 200 patients of dengue viral infection (120 males, 80 females) were included in this prospective descriptive study. The blood samples of the individuals were first screened for malaria by blood smear examination and then the negative samples were tested by anti-dengue IgM strip. The strip positive cases were further screened by IgM capture ELISA and their complete blood count including hemoglobin estimation (Hb), total and differential leukocyte counts (TLC and DLC), erythrocyte sedimentation rate (ESR) and platelet counts were performed. On the basis of the severity of signs and symptoms, dengue virus infected patients were subdivided into dengue fever (DF) and dengue hemorrhagic fever (DHF) comprising 70 and 100 confirmed patients, respectively. On the other hand, 30 patients were found infected with Malaria while overall 120 patients showed thrombocytopenia. The patients of DHF were found to have more leucopenia, raised hemoglobin level and thrombocytopenia < 50,000/µl compared to the patients belonging to DF and malaria. On the basis of the outcomes of the study, it was concluded that patients affected by DF were at a lower risk of undergoing haematological disturbance than suffering from DHF. While, the patients infected by Malaria were found to have no significant change in their blood components.

Keywords: dengue fever, blood, serum, malaria, ELISA

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Authors: Bo Wang

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This paper proposes a method that can estimate PM2.5 by the images of GF-1 Satellite that called WFOV images (Wide Field of View). AOD (Aerosol Optical Depth) over land surfaces was retrieved in Shanghai area based on DDV (Dark Dense Vegetation) method. PM2.5 information, gathered from ground monitoring stations hourly, was fitted with AOD using different polynomial coefficients, and then the correlation coefficient between them was calculated. The results showed that, the GF-1 WFOV images can meet the requirement of retrieving AOD, and the correlation coefficient between the retrieved AOD and PM2.5 was high. If more detailed and comprehensive data is provided, the accuracy could be improved and the parameters can be more precise in the future.

Keywords: remote sensing retrieve, PM 2.5, GF-1, aerosol optical depth

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Authors: Thanutch Sukwimolseree, Preeyaphorn Kosa

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Many problems are occurred in watershed due to human activity and economic development. The purpose is to determine the effects of the land use change on surface runoff using land use map on 1980, 2001 and 2008 and daily weather data during January 1, 1979 to September 30, 2010 applied to SWAT. The results can be presented that the polynomial equation is suitable to display that relationship. These equations for land use in 1980, 2001 and 2008 are consisted of y = -0.0076x5 + 0.1914x4–1.6386x3 + 6.6324x2–8.736x + 7.8023(R2 = 0.9255), y = -0.0298x5 + 0.8794x4 - 9.8056x3 + 51.99x2 - 117.04x + 96.797; (R2 = 0.9186) and y = -0.0277x5 + 0.8132x4 - 8.9598x3 + 46.498x2–101.83x +81.108 (R2 = 0.9006), respectively. Moreover, if the agricultural area is the largest area, it is a sensitive parameter to concern surface runoff.

Keywords: land use, runoff, SWAT, upper Mun River basin

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Authors: Negar Riazifar, Nigel G. Stocks

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This paper proposes strategies in level crossing (LC) sampling and reconstruction that provide alias-free high-fidelity signal reconstruction for speech signals without exponentially increasing sample number with increasing bit-depth. We introduce methods in LC sampling that reduce the sampling rate close to the Nyquist frequency even for large bit-depth. The results indicate that larger variation in the sampling intervals leads to an alias-free sampling scheme; this is achieved by either reducing the bit-depth or adding jitter to the system for high bit-depths. In conjunction with windowing, the signal is reconstructed from the LC samples using an efficient Toeplitz reconstruction algorithm.

Keywords: alias-free, level crossing sampling, spectrum, trigonometric polynomial

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Authors: Dia I. Abu-Al-Nadi, M. J. Mismar, T. H. Ismail

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A technique for estimating the direction-of-arrival (DOA) of unknown number of source signals is presented using the eigen-approach. The eigenvector corresponding to the minimum eigenvalue of the autocorrelation matrix yields the minimum output power of the array. Also, the array polynomial with this eigenvector possesses roots on the unit circle. Therefore, the pseudo-spectrum is found by perturbing the phases of the roots one by one and calculating the corresponding array output power. The results indicate that the DOAs and the number of source signals are estimated accurately in the presence of a wide range of input noise levels.

Keywords: array signal processing, direction-of-arrival, antenna arrays, Eigenvalues, Eigenvectors, Lagrange multiplier

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Authors: M. Helaimi, R. Taleb, D. Benyoucef, B. Belmadani

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This paper presents the design of a polynomial controller with coefficient diagram method (CDM). This controller is used to control the output power of high frequency resonant inverter with LLC tank. One of the most important problems associated with the proposed inverter is achieving ZVS operating during the induction heating process. To overcome this problem, asymmetrical voltage cancellation (AVC) control technique is proposed. The phased look loop (PLL) is used to track the natural frequency of the system. The small signal model of the system with the proposed control is obtained using extending describing function method (EDM). The validity of the proposed control is verified by simulation results.

Keywords: induction heating, AVC control, CDM, PLL, resonant inverter

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Authors: Shubham Jaiswal

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In the present article, a drive is taken to compute the solution of spatial fractional order advection-dispersion equation having source/sink term with given initial and boundary conditions. The equation is converted to a system of ordinary differential equations using second-kind shifted Chebyshev polynomials, which have finally been solved using finite difference method. The striking feature of the article is the fast transportation of solute concentration as and when the system approaches fractional order from standard order for specified values of the parameters of the system.

Keywords: spatial fractional order advection-dispersion equation, second-kind shifted Chebyshev polynomial, collocation method, conservative system, non-conservative system

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Authors: Ilija Plecas, Dalibor Arbutina

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The leaching rate of 60Co from spent mix bead (anion and cation) exchange resins in a cement-bentonite matrix has been studied. Transport phenomena involved in the leaching of a radioactive material from a cement-bentonite matrix are investigated using three methods based on theoretical equations. These are: the diffusion equation for a plane source, an equation for diffusion coupled to a first order equation and an empirical method employing a polynomial equation. The results presented in this paper are from a 25-year mortar and concrete testing project that will influence the design choices for radioactive waste packaging for a future Serbian radioactive waste disposal center.

Keywords: cement, concrete, immobilization, leaching, permeability, radioactivity, waste

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Authors: Clarissa Valença Travassos da Silva

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In this article, it is intended to study the book “The unbearable Lightness of Being” by the Czech Republican writer Milan Kundera. The main objective is to be an interdisciplinary study basis for students in the world about love and politics at old communist Czechoslovakia. Love is presented by discussing the relationship between Tomas and Tereza and the discovery of true love. Furthermore, it is debated the Russian invasion in Czechoslovakia and the outcomes of it for the personages, all this related to the contradiction of lightness and heaviness in life. For the production of this didactic material, the researcher based her work on the original book, “The Unbearable Lightness of Being” by Kundera, Milan Kundera’s interviews, Friedrich Nietzche, Zygmunt Bauman and George Orwell, among Brazilian and international articles on the issue.

Keywords: lightness, heaviness, Russia, Czechoslovakia, love

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Authors: Kyu Jin Kim, Byung Kwan Oh, Hyo Seon Park

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The seismic responses-based structural health monitoring system has been performed to reduce seismic damage. The inter-story drift ratio which is the major index of the seismic capacity assessment is employed for estimating the seismic damage of buildings. Meanwhile, seismic response analysis to estimate the structural responses of building demands significantly high computational cost due to increasing number of high-rise and large buildings. To estimate the inter-story drift ratio of buildings from the earthquake efficiently, this paper suggests the estimation method of inter-story drift for buildings using an artificial neural network (ANN). In the method, the radial basis function neural network (RBFNN) is integrated with optimization algorithm to optimize the variable through evolutionary learning that refers to evolutionary radial basis function neural network (ERBFNN). The estimation method estimates the inter-story drift without seismic response analysis when the new earthquakes are subjected to buildings. The effectiveness of the estimation method is verified through a simulation using multi-degree of freedom system.

Keywords: structural health monitoring, inter-story drift ratio, artificial neural network, radial basis function neural network, genetic algorithm

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Authors: Zuhier Altawallbeh

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This paper investigates the approximate analytical solutions of general form of Volterra integro-differential equations system by using the residual power series method (for short RPSM). The proposed method produces the solutions in terms of convergent series requires no linearization or small perturbation and reproduces the exact solution when the solution is polynomial. Some examples are given to demonstrate the simplicity and efficiency of the proposed method. Comparisons with the Laplace decomposition algorithm verify that the new method is very effective and convenient for solving system of pantograph equations.

Keywords: integro-differential equation, pantograph equations, system of initial value problems, residual power series method

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Authors: Young Hee Geum

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In this paper,we develop the complex dynamics of a family of optimal fourth-order multiple-root solvers and plot their basins of attraction. Mobius conjugacy maps and extraneous fixed points applied to a prototype quadratic polynomial raised to the power of the known integer multiplicity m are investigated. A 300 x 300 uniform grid centered at the origin covering 3 x 3 square region is chosen to visualize the initial values on each basin of attraction in accordance with a coloring scheme based on their dynamical behavior. The illustrative basins of attractions applied to various test polynomials and the corresponding statistical data for convergence are shown to confirm the theoretical convergence.

Keywords: basin of attraction, conjugacy, fourth-order, multiple-root finder

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Authors: H. Gonzalez-Rivera, J. L. Palmeros-Torres

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This paper describes the application of traditional computer vision techniques as a procedure for automatic measurement of the secondary dendrite arm spacing (SDAS) from microscopic images. The algorithm is capable of finding the lineal or curve-shaped secondary column of the main microstructure, measuring its length size in a micro-meter and counting the number of spaces between dendrites. The automatic characterization was compared with a set of 1728 manually characterized images, leading to an accuracy of −0.27 µm for the length size determination and a precision of ± 2.78 counts for dendrite spacing counting, also reducing the characterization time from 7 hours to 2 minutes.

Keywords: dendrite arm spacing, microstructure inspection, pattern recognition, polynomial regression

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